In general, electron paramagnetic resonance (EPR) is used to study materials with unpaired electrons by exciting electron spins with magnetic fields and then measuring the field generated by the relaxation of the electrons. EPR can be conducted using continuous wave (CW) excitation (varying strength of an applied magnetic field) or pulsed excitation (pulsed microwave fields inducing a magnetic field) applied to the electrons. As any of these excitation sources is scanned, or varied, across a range, there comes an energy of excitation that causes the electron spins to flip and this magnetic absorption or resonance is seen as an absorption maximum in the EPR signal spectrum. By identifying excitation energies associated with the observed absorption maximum or maxima, one can identify characteristics of the material being studied.
Rapid Scan (RS) EPR is a recently developed CW method that combines narrowband excitation and broadband detection. In RS EPR, sinusoidal magnetic field scans that span the entire EPR spectrum cause electron spin excitations twice during the scan period. Periodic transient RS signals are digitized and time-averaged. Deconvolution of these RS signals is required in order to identify their relevant characteristics and distinguish the RS signals from background noise. Deconvolution of absorption spectrum from the measured full-cycle signal is an ill-posed problem (a unique solution may not exist or/and be unstable) that does not have a stable solution because the magnetic field passes the same EPR line twice per sinusoidal scan during up- and down-field passages. As a result, RS signals consist of two contributions that need to be separated and postprocessed individually. Deconvolution of either of the contributions is a well-posed problem that has a stable solution. Prior methods solve the separation problem by cutting the full-scan signal into two half-period pieces and then using an algorithm to deconvolve each separately. However, such prior methods impose undesired limitations on RS EPR experiments. Therefore, a need exists to improve upon the existing methods.